What's the point of Cell Dingbats?

Echo uses a special CellDingbat as a visual indicator to distinguish the "Echo" cells from the normal "Output" cells. One can mimic them using, e.g.,

CellPrint @ Cell[BoxData["Test"], "Print"
  , CellDingbat -> Replace[CellDingbat, CurrentValue[{StyleDefinitions, "Echo"}]]]

Hence CellDingbats are useful to visually differentiate between different kinds of in- or output cells.

They can be used for bullet lists.

There's no limitation on what or how many characters you can use. See the CellDingbat option.

In making notebooks intended to be seen by other people, I often use the watch cell dingbat to indicate that the code in that particular input cell will take a long time to evaluate. Less often, I use the light bulb one to emphasize a cell with particularly neat code. Otherwise, like Szabolcs, I use them for bullets.